Sensing logic is essentially (deep) critical thinking involving:
1. Sensing contradictions. or cognitive dissonance. that something cannot be true and false at the same time.
2. Sensing that there is a right path to follow. that there are laws that govern the universe. Sensing in your GUT for a grand unifying theory. that there is an order to our deepest fears.
3. Sensing why logic always seem to work out and is consistent.
4. Sensing the fastest/laziness way to get the answer/objective. (of course within moral boundaries). aka principle of least work done.
5. Sensing the importance of root foundation, assumptions, values and beliefs as how everything stems to flow from them.
6. A sense of inquiry to ask why, rebel, and question societal norms and assumptions. The dissatisfaction/burden to ask why and seek answers for problem solving. Questioning plays a big part of intuition.
7. A sense of conviction and cohesion vs gaps and lack of cohesion in the flow of arguments. Looking back and reflecting to check the flow of arguments.
8. A sense of abstraction and extension.
9. A sense of quantification and categorization, portioning and percentage. what about subitization?
Let me try to define artistic intuition:
1. accepting/absorptive of words, language, literature from social norms/influences and what people say. (trusting first before questioning. the purpose of questioning is for imagination and not to question the norm assumptions. accepting of social norms. there must have been a (good) reason why society is/was inclined to that standard).
2. myriad spontaneous bubbling of random ideas with emotions in the expression of artifact/speech/communication. ability to see pictures/colours/tune/rhythm/moves in the mind.
3. (broad?) critical thinking ie. analysis inclined towards the study of human nature. cf. inanimate nature (science).